Formulate the situation as a system of two linear equations in two variables. be sure to state clearly the meaning of your x- and y-variables. solve the system by the elimination method. be sure to state your final answer in terms of the original question.
a lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. if the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?
x = $4,000 investors
y =
$8,000 investors
solve the system by row-reducing the corresponding augmented matrix. (enter your answers as a comma-separated list. if the system is inconsistent, enter inconsistent. if the system is dependent, enter dependent.)
leftbrace2.gif
2x + y = 17
x + y = 13
the situation as a system of two linear equations in two variables. be sure to state clearly the meaning of your x- and y-variables. solve the system by the elimination method. be sure to state your final answer in terms of the original question.
a jar contains 80 nickels and dimes worth $6.80. how many of each kind of coin are in the jar?
x = nickels
y = dimes

1) There were 33 $4,000 investors and 27 $8,000 investors.

2) The solution in x = 4, y = 9.

3) There were 24 nickels and 56 dimes.

Step-by-step explanation:

1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?

I am going to say that:

x is the number of investors that contributed 4,000.

y is the number of investors that contributed 8,000.

Building the system:

There are 60 investors. So:

In all, the partnership raised $348,000. So:

I am going to simplify by 4000. So:

Solving the system:

The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:

I am going to multiply 1) by -1. So we have

By addition, the x are going to cancel each other

For x:

There were 33 $4,000 investors and 27 $8,000 investors.

2) Solve the system by row-reducing the corresponding augmented matrix.

This system has the following augmented matrix:

To help the row reducing, i am going to swap the first with the second line:

So we have:

Now, reducing the first column.

So we have:

Now we do:

And the matrix is:

Now to reduce the second column, we do:

.

So the solution is:

x = 4, y = 9.

3) A jar contains 80 nickels and dimes worth $6.80. How many of each kind of coin are in the jar?

I am going to say that x is the number of nickels and y is the number of dimes.

Each nickel is worth 5 cents and each dime is worth 10 cents.

Building the system:

There are 80 coins in all:

They are worth $6.80. So:

Solving the system:

I am going to divide 1) by -10, so we can cancel y. So:

Adding:

*(-100)

Also

There were 24 nickels and 56 dimes.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720